I'm also very interested in this especially as some Pyload plugins just aren't getting fixed. From what I've read on the JD forums, headless support is low priority even for Jdownloader 2 which is currently in beta. Would be really cool if you could walk Linux newbies like me through installation. I've read some info on this but I can't find it anymore and I couldn't get SCREEN to run properly anyway. Thx.

I reed this post and tried it by myselve.
I used
vnc4server caues it includes Xwindows output
openjava
(Xfce »Installation was not to 100% cause tty0 is missing)
jd.sh to install Jdownloader in version 1.

This allow me to connect using VNC viewer and getting a comand prompt.
Installing and upgrade Jdownloader has taken ~45 mins

Positive:
Jdownloader can be used via VNC like it is on Windows.Web Interface is available and work fine (Can be accessable from any computer in the network)

Negative:
Sloooowwww.. Response
Unrar from JD package is not working proper cause it is X86 binary
JD starts downloading based on the Max DLs. setting and stops.. (Maybe it is case the HD spins down)
Samba is not responsing properly while JD is running (3MB vs 60 MB to Windows